Mathematics
Grade10
Easy
Question
What are the equations of the asymptotes of the function f(x) = 
+ 3 ?
- Horizontal: y = 5 , Vertical : x = 3
- Horizontal: y = -3 , Vertical : x = 5
- Horizontal: x = 5 , Vertical : y = -3
- Horizontal: x = -3 , Vertical : y = 5
Hint:
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.
The correct answer is: Horizontal: y = -3 , Vertical : x = 5
Here, we have to find the asymptotes to the graph y = 1/(x-5) +3.
For the function, f(x) = 
+ k
Horizontal asymptote: y = k
Vertical asymptote: x = h
In this case, asymptotes are x = 5 and y = -3.
Hence, the correct option is B.
Horizontal asymptote is y = k and vertical asymptote is x = h, where (h,k) is a moving point on the graph.
